Kompany is facing another month on the sidelines after suffering a reaction on his return from injury against Sunderland on St Stephen’s Day.
The Belgian’s current lay-off is his 12th for a calf injury since the start of the title-winning 2011-12 campaign and his third this season.
He has also missed games because of hamstring and groin injuries in recent years and City’s medical department want to analyse the problems deeper.
Speaking ahead of tomorrow’s trip to Watford, Pellegrini said: “We are trying to do all (we can) to know how we can help Vincent to try to be fit and not to continue with the same calf problems. So, everything the club can do, we are going to do it.”
Kompany’s influence on the City side is huge and the team need him fit to bolster their Premier League title bid in the second half of the season.
In the nine Premier League games in which he has featured this term, City have kept seven clean sheets and not lost. City have lost five of the 10 games he has missed and conceded in nine of them.
Despite that, and concerns Kompany may suffer further problems, Pellegrini has no intention of bringing in extra defensive cover in the January transfer window.
The Chilean said: “No, really I think the squad is complete. As always, I said that we are not going to close the window but we are not really thinking of any special players to bring in.”
In terms of positive injury news, midfielder Fabian Delph and left-back Gael Clichy are both back in contention for tomorrow’s trip to Watford after missing Tuesday’s goalless draw at Leicester.
Pellegrini said: “Fabian Delph and Clichy have worked normally. They had some small problems in the last game.”
Pellegrini has given his squad permission to enjoy their New Year celebrations - but warned them not to stay up too late.
Asked if his players faced an early curfew, Pellegrini said: “No, not before midnight. All of them must celebrate New Year’s Eve but I think they can do it early - maximum one o’clock.”
Meanwhile, Watford boss Quique Sanchez Flores has much to smile about heading into the new year - but that did not stop him having to console his son following the recent defeat to Tottenham.
The Hornets sit ninth in the Premier League having been promoted in the summer and are just two points behind fifth-placed Crystal Palace, but they suffered defeat to Spurs after a controversial 89th-minute goal on Monday.
With the scores level at 1-1 despite Watford being down to 10 men following a red card for Nathan Ake, Son Heung-min bagged a late winner for the visitors to Vicarage Road despite appearing to be offside in the build-up.
The result left Sanchez Flores’ son Paulo in tears, but he was soon being told to look on the bright side of life by his chirpy father.
“I’m always thinking we need to keep our minds and that is important because we don’t want to lose our perspective,” he said. “But we have lots of reasons to be happy. After the last match, one of my kids Paulo was crying because we lost in the last minute and I found very quickly 10 reasons to be happy with Watford.
“In seconds I found maybe 10 or 12 reasons to say ‘Paulo, we need to be happy’. We are competitive, we have a good connection with the fans, they are happy, we are in a good position, we are playing well and have the possibility to win a lot. We have 29 points and are really close to the objective.
“So we have a lot of reasons to be happy, I don’t have any reason to be sad.”